论文标题
通过符号高斯波数据包动力学对半经典期望值的近似
Approximation of Semiclassical Expectation Values by Symplectic Gaussian Wave Packet Dynamics
论文作者
论文摘要
本文涉及以高斯作为初始条件为半经典的schrödinger方程的解决方案的位置和动量的期望值的近似值。特别令人感兴趣的是通过我们对高斯波数据包动力学的符号/哈密顿公式获得的近似值，该制定使用Hagedorn和其他人使用经典的Hamiltonian系统对常规配方进行了校正项。主要结果是证明我们的公式给出了比经典公式在某些条件下对潜在函数的期望值动态的更高近似值。具体而言，由于半经典参数$ \ varepsilon $接近$ 0 $，我们的动力学给出了期望值动力学的$ O（\ varepsilon^{3/2}）$近似值，而经典的动力学给出了$ O（\ varepsilon）$近似值。
This paper concerns an approximation of the expectation values of the position and momentum of the solution to the semiclassical Schrödinger equation with a Gaussian as the initial condition. Of particular interest is the approximation obtained by our symplectic/Hamiltonian formulation of the Gaussian wave packet dynamics that introduces a correction term to the conventional formulation using the classical Hamiltonian system by Hagedorn and others. The main result is a proof that our formulation gives a higher-order approximation than the classical formulation does to the expectation value dynamics under certain conditions on the potential function. Specifically, as the semiclassical parameter $\varepsilon$ approaches $0$, our dynamics gives an $O(\varepsilon^{3/2})$ approximation of the expectation value dynamics whereas the classical one gives an $O(\varepsilon)$ approximation.
